Performance of multicomputers largely depends on that of the underlying network communications such as multicast. Two major parameters used to evaluate multicast routing are the time it takes to deliver the message to all destinations and the traffic which refers to the total number of links involved. Mesh is a network topology widely used in multicomputers. It has been proved that, in mesh network, it is NP-hard to find the multicast routing which is optimal on both time and traffic. In this paper, we proposed two efficient multicast algorithms designed for store-and-forward switched mesh-connected multicomputers: DIAG and DDS. They are both tree-based shortest path multicast algorithms whose complexity is O(KN) or less. Performance evaluations of these algorithms resulted from simulations are given at the end.